Thousands of the airline's cabin crewmembers said Sunday they would walk out Jan. 29-31, threatening travel chaos for airline customers.
The Transport and General Workers Union warned of two other stoppages Feb. 5-7 and Feb. 12-14 unless the dispute is resolved, the airline's Web site said Monday.
Airline Chief Executive Willie Walsh said a strike was "unjustified." He blamed excessive union demands for the failure of the talks.
The cabin crew complained rules introduced 18 months ago forced members to work when they were ill, The Independent reported. BA insisted it simply sought to reduce high levels of absences.
Customers who booked flights for Jan. 29 through Feb. 16 can change their flight dates without penalty, with certain restrictions, the airline said.
A strike next week would be the first by cabin crews since July 1997. That three-day strike cost the airline $250 million.